Problem: Solve for $x$ and $y$ using elimination. ${3x+y = 33}$ ${5x+3y = 63}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-3$ ${-9x-3y = -99}$ $5x+3y = 63$ Add the top and bottom equations together. $-4x = -36$ $\dfrac{-4x}{{-4}} = \dfrac{-36}{{-4}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {3x+y = 33}\thinspace$ to find $y$ ${3}{(9)}{ + y = 33}$ $27+y = 33$ $27{-27} + y = 33{-27}$ ${y = 6}$ You can also plug ${x = 9}$ into $\thinspace {5x+3y = 63}\thinspace$ and get the same answer for $y$ : ${5}{(9)}{ + 3y = 63}$ ${y = 6}$